Excitation-Density-Controlled Regimes of Collective Light-Matter Dynamics

Area of Science:

• Quantum Optics
• Condensed Matter Physics
• Theoretical Chemistry

Background:

• Collective light-matter dynamics are crucial in quantum optics and condensed matter.
• Mean-field (MF) and single-excitation (SE) approximations are commonly used but lack clear parameter delineations.
• Understanding the validity of these approximations is essential for accurate theoretical modeling.

Purpose of the Study:

• To delineate the parameter regimes where MF and SE approximations are valid for collective light-matter dynamics.
• To identify key parameters governing the accuracy of these theoretical descriptions.
• To provide a clear map for selecting appropriate theoretical models.

Main Methods:

• Analysis of the Tavis-Cummings model.
• Characterization of limiting regimes using the number of molecules (N) and excitation number (Nexc).
• Application of cluster expansion to investigate beyond-MF correlations and vibronic interactions.

Main Results:

• MF and SE approximations agree in the N ≫ 1 and zero excitation density limit, showing linear dynamics and harmonic Rabi oscillations.
• At finite excitation density, MF dynamics become nonlinear, described by a Duffing equation with anharmonic Rabi frequency.
• Inclusion of vibronic interactions leads to a linear collective limit for both approximations, via polaron decoupling (SE) and linearization (MF).

Conclusions:

• A two-parameter regime map (N and Nexc) clarifies the validity of MF and SE approximations in collective light-matter dynamics.
• The study reveals distinct linear and nonlinear dynamics regimes based on excitation density.
• This work provides essential insights for theoretical modeling of quantum systems interacting with light.